As per the records of the World Health Organization, the first formally reported incidence of Zika virus occurred in Brazil in May 2015. The disease then rapidly spread to other countries in Americas and East Asia, affecting more than 1,000,000 people. Zika virus is primarily transmitted through bites of infected mosquitoes of the species Aedes (Aedes aegypti and Aedes albopictus). The abundance of mosquitoes and, as a result, the prevalence of Zika virus infections are common in areas which have high precipitation, high temperature, and high population density. Nonlinear spatio‐temporal dependency of such data and lack of historical public health records make prediction of the virus spread particularly challenging. In this article, we enhance Zika forecasting by introducing the concepts of topological data analysis and, specifically, persistent homology of atmospheric variables, into the virus spread modeling. The topological summaries allow for capturing higher order dependencies among atmospheric variables that otherwise might be unassessable via conventional spatio‐temporal modeling approaches based on geographical proximity assessed via Euclidean distance. We introduce a new concept of cumulative Betti numbers and then integrate the cumulative Betti numbers as topological descriptors into three predictive machine learning models: random forest, generalized boosted regression, and deep neural network. Furthermore, to better quantify for various sources of uncertainties, we combine the resulting individual model forecasts into an ensemble of the Zika spread predictions using Bayesian model averaging. The proposed methodology is illustrated in application to forecasting of the Zika space‐time spread in Brazil in the year 2018.

中文翻译：

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用拓扑数据分析对寨卡病毒时空传播进行集合预报

根据世界卫生组织的记录，2015 年 5 月巴西首次正式报告寨卡病毒的发病率，随后该疾病迅速蔓延至美洲和东亚其他国家，影响超过 1,000,000 人。寨卡病毒主要通过被感染的伊蚊（埃及伊蚊和白纹伊蚊）蚊子叮咬传播。蚊子数量众多，因此，寨卡病毒感染的流行在降水量大、温度高和人口密度高的地区很常见。此类数据的非线性时空依赖性以及缺乏历史公共卫生记录使得对病毒传播的预测特别具有挑战性。在本文中，我们通过介绍拓扑数据分析的概念来增强寨卡病毒的预测，特别是 大气变量的持久同源性，进入病毒传播建模。拓扑摘要允许捕获大气变量之间的高阶依赖关系，否则这些依赖关系可能无法通过基于通过欧几里德距离评估的地理邻近度的传统时空建模方法进行评估。我们引入了累积 Betti 数的新概念，然后将累积 Betti 数作为拓扑描述符整合到三个预测机器学习模型中：随机森林、广义增强回归和深度神经网络。此外，为了更好地量化各种不确定性来源，我们使用贝叶斯模型平均将由此产生的单个模型预测组合成寨卡病毒传播预测的集合。